It is the obvious conclusion from events of recent weeks: transparency matters. And yet that wisdom continues to elude the prime minister, as he demonstrated last week when announcing the terms of a new inquiry into the Iraq war.

Its aim to identify "lessons to be learnt" is laudable. Its authority to call witnesses and examine documents is impressive. But the plan to conduct most of it in secret is profoundly wrong.

There is a superficially appealing justification. Civil servants, ministers and intelligence officers may be more candid in private. A little discretion, goes this argument, is a fair price for a more truthful account of things.

But that view contains the peculiar assumption that senior officials only lie in public. It recognises the gentlemen's agreement by which Sir Principal Private Secretary will answer Lord Sinecure's questions candidly in camera, but not on camera.

That sort of informal covenant, highly esteemed in Westminster, means nothing to the rest of the country. It is of a piece with the honesty box approach that governed MPs' expenses, now exposed as a scam.

Once made aware of the awkward parallel, Gordon Brown belatedly allowed Sir John Chilcot, the inquiry chair, some leeway to hold sessions in public. But another lesson from the expenses scandal is that partial disclosure arouses as much suspicion of a cover-up as it dispels. There can be no half-measures. If individuals in the Iraq inquiry want to dodge questions and dissemble, let them try to do so in full public view.

The government's weary reluctance to embark on that process is understandable up to a point. Iraq has hardly been swept under the carpet. Two parliamentary committees and two independent inquiries have investigated aspects of the war. Their combined reports afford a fairly rich narrative of events. Is there anything still to come out?

The answer, judging by revelations in today's Observer, is "yes". Tony Blair, it transpires, has made clear to Mr Brown his wish for the new inquiry to be held in private. The very fact of that intervention - a covert bid by the central player to fix the game - demonstrates the need for more open hearings. So does the revelation of plans, hatched by the Bush administration, to provoke Baghdad into an act of military aggression.

The public has never been told exactly when it was that Mr Blair committed Britain to a US-led war to effect regime change in Baghdad. If, as is widely suspected, it was April 2002, then the ensuing year of public persuasion, weapons inspection and UN diplomacy was a sham, a deception to accommodate the British people in a secret pact with the White House. Such a grave allegation must be definitively refuted or proven - in public.

That is a specific reason for a public inquiry. A general one is contained in Mr Brown's statement to Parliament on constitutional renewal earlier this month: "We cannot move our country forward unless we break with these old practices and the old ways."

He might easily have been referring to the culture of secrecy and contempt for public opinion within the political machine that took Britain to war in Iraq. As it happens, he was talking about expenses.

A week later, MPs' receipts were published with crucial details blacked out. The facts had already been leaked, so official publication was symbolic. It should have been a gesture of transparency, a ceremonial flinging open of doors. For Parliament to make it the opposite took exceptional collective stupidity.

Mr Brown also said in his statement: "It will be what we now do, not just what we say, that will prove we have learnt and that we have changed."

Quite so. And by holding the Iraq inquiry in private Mr Brown will again prove that, when it comes to transparency, his government has not changed and has learnt nothing.